Article

Local Boundary Value Problems for a Degenerate Loaded Equation of Parabolic-Hyperbolic Type of the Second Kind

B. I. IslomovDepartment of Differential Equations and Mathematical Physics, National University of Uzbekistan, 100174, Tashkent, UzbekistanDildora NasirovaDepartment of Higher Mathematics, Tashkent State Technical University, Tashkent, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2023en

ABI

Abstract

In the present paper, we pose and study local boundary value problems for a parabolic-hyperbolic equation of the second kind with degeneration and a loaded part. The problem is reduced to a simpler problem, and regular solvability is studied in one part of the domain, and generalized solvability – in the other part of the domain. The method of energy integrals and the method of integral equations are applied. Theorems on the existence and uniqueness of a solution to the problem are proved.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods advanced mathematical theories

Identifiers

DOI: 10.1134/s1995080223120168

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